A car traveling at a speed of 30.0m/s encounters an emergency and comes to a complete stop. How much time will it take for the car to stop if it decelerates at -4.0m/s

We can solve this problem using the equation of motion:

\[
v_f = v_i + at
\]

Where:
- \( v_f \) is the final velocity (0 m/s, since the car comes to a stop),
- \( v_i \) is the initial velocity (30.0 m/s),
- \( a \) is the acceleration (-4.0 m/s², since the car is decelerating),
- \( t \) is the time it takes to stop (what we are solving for).

Rearranging the equation to solve for \( t \):

\[
t = \frac{v_f - v_i}{a}
\]

Substitute the given values:

\[
t = \frac{0 - 30.0}{-4.0} = \frac{-30.0}{-4.0} = 7.5 \, \text{seconds}
\]

So, the car will take **7.5 seconds** to come to a complete stop.

Would you like more details or have any questions?

Here are five related questions for deeper understanding:
1. What is the stopping distance of the car given the same conditions?
2. How would the stopping time change if the deceleration were different?
3. What would happen to the stopping time if the car were moving at a higher speed?
4. How do factors like road conditions affect the deceleration rate?
5. How does the mass of the car influence its deceleration?

**Tip:** When dealing with deceleration, always remember that acceleration is negative because it opposes the direction of motion.

A car traveling at a speed of 30.0m/s encounters an emergency and comes to a complete stop. How much time will it take for the car to stop if it decelerates at -4.0m/s²?

Learn how to calculate the time it takes for a car traveling at 30.0 m/s to stop with a deceleration of -4.0 m/s² using the equation of motion. This physics problem explores key concepts in kinematics and linear motion, suitable for students in Grades 9-12.

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